Maximum ratio transmission

ABSTRACT

An arrangement where a transmitter has a plurality of transmitting antennas that concurrently transmit the same symbol, and where the signal delivered to each transmitting antenna is weighted by a factor that is related to the channel transmission coefficients found between the transmitting antenna and receiving antennas. In the case of a plurality of transmit and a transmit antenna I is h i , the weighting factor is h i * divided by a normalizing factor, a, which is  
           (       ∑     k   =   1     K     ⁢            h   k          2       )       1   /   2       ,       
 
where K is the number of transmitting antennas. When more than one receiving antenna is employed, the weighting factor is  
           1   a     ⁢       (   gH   )     H       ,       
 
where g=[g 1  . . . g L ), H is a matrix of channel coefficients, and a is a normalizing factor  
           (         ∑     p   =   l     L     ⁢     ∑     q   =   l     L       |       ∑     k   =   l     K     ⁢       h     p   ⁢           ⁢   k       ⁢     h   qk   *           )       1   /   2       .

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 10/963,838 filed on Oct. 12, 2004, which is a continuation of U.S. patent application Ser. No. 10/177,461 filed on Jun. 19, 2002, now U.S. Pat. No. 6,826,236, issued on Nov. 30, 2004, which is a continuation of U.S. patent application Ser. No. 09/156,066 filed on Sep. 17, 1998, now U.S. Pat. No. 6,459,740, issued on Oct. 1, 2002, each of which is incorporated by reference in their entirety herein.

FIELD OF ART

Aspects described herein relate to a system and method for using transmit diversity in a wireless communications setting.

BACKGROUND OF THE INVENTION

Wireless communications services are provided in different forms. For example, in satellite mobile communications, communications links are provided by satellite to mobile users. In land mobile communications, communications channels are provided by base stations to the mobile users. In PCS, communications are carried out in microcell or picocell environments, including outdoors and indoors. Regardless the forms they are in, wireless telecommunication services are provided through radio links, where information such as voice and data is transmitted via modulated electromagnetic waves. That is, regardless of their forms, all wireless communications services are subjected to vagaries of the propagation environments.

The most adverse propagation effect from which wireless communications systems suffer is the multipath fading. Multipath fading, which is usually caused by the destructive superposition of multipath signals reflected from various types of objects in the propagation environments, creates errors in digital transmission. One of the common methods used by wireless communications engineers to combat multipath fading is the antenna diversity technique, where two or more antennas at the receiver and/or transmitter are so separated in space or polarization that their fading envelopes are de-correlated. If the probability of the signal at one antenna being below a certain level is p (the outage probability), then the probability of the signals from L identical antennas all being below that level is p^(L). Thus, since p<1, combining the signals from several antennas reduces the outage probability of the system. The essential condition for antenna diversity schemes to be effective is that sufficient de-correlation of the fading envelopes be attained.

A classical combining technique is the maximum-ratio combining (MRC) where the signals from received antenna elements are weighted such that the signal-to-noise ratio (SNR) of their sum is maximized. The MRC technique has been shown to be optimum if diversity branch signals are mutually uncorrelated and follow a Rayleigh distribution. However, the MRC technique has so far been used exclusively for receiving applications. As there are more and more emerging wireless services, more and more applications may require diversity at the transmitter or at both transmitter and receiver to combat severe fading effects. As a result, the interest in transmit diversity has gradually been intensified. Various transmit diversity techniques have been proposed but these transmit diversity techniques were built on objectives other than to maximize the SNR. Consequently, they are sub-optimum in terms of SNR performance.

SUMMARY OF THE INVENTION

Improved performance is achieved with an arrangement where the transmitter has a plurality of transmitting antennas that concurrently transmit the same symbol, and where the signal delivered to each transmitting antenna is weighted by a factor that is related to the channel transmission coefficients found between the transmitting antenna and receiving antenna(s). In the case of a plurality of transmit antennas and one receive antenna, where the channel coefficient between the receive antenna and a transmit antenna i is h_(i), the weighting factor is h_(i)* divided by a normalizing factor, a, which is ${a = \left( {\sum\limits_{k = 1}^{K}{h_{k}}^{2}} \right)^{1/2}},$ where K is the number of transmitting antennas. When more than one receiving antenna is employed, the weighting factor is ${\frac{1}{a}({gH})^{H}},$ where g=[g₁ . . . g_(L)], H is a matrix of channel coefficients, and a is a normalizing factor $\left( {\sum\limits_{p = 1}^{L}\sum\limits_{q = 1}^{L}} \middle| {\sum\limits_{k = 1}^{K}{h_{p\quad k}h_{qk}^{*}}} \right)^{1/2}.$

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an arrangement where there is both transmit and receive diversity.

FIG. 2 is a flowchart illustrating a routine performed at the transmitter of FIG. 1.

FIG. 3 is a flowchart illustrating a routine performed at the receiver of FIG. 1.

DETAILED DESCRIPTION

FIG. 1 depicts a system which comprises K antennas for transmission and L antennas for reception. The channel between the transmit antennas and the receive antennas can be modeled by K×L statistically-independent coefficients, as show in FIG. 1. It can conveniently be represented in matrix notation by $\begin{matrix} {H = {\begin{pmatrix} h_{11} & \cdots & \cdots & \cdots & h_{1K} \\ \vdots & ⋰ & \quad & \quad & \vdots \\ \vdots & \quad & ⋰ & \quad & \vdots \\ \vdots & \quad & \quad & ⋰ & \vdots \\ h_{L\quad 1} & \cdots & \cdots & \cdots & h_{LK} \end{pmatrix} = \begin{pmatrix} h_{1} \\ \vdots \\ \vdots \\ \vdots \\ h_{L} \end{pmatrix}}} & (1) \end{matrix}$ where the entry h_(pk) represents the coefficient for the channel between transmit antenna k and receiver antenna p. It is assumed that the channel coefficients are available to both the transmitter and receiver through some means, such as through a training session that employs pilot signals sent individually through each transmitting antenna (see block 202 of FIG. 2 and block 302 of FIG. 3). Since obtaining these coefficients is well known and does not form a part of this invention additional exposition of the process of obtaining the coefficients is deemed not necessary.

The system model shown in FIG. 1 and also in the routines of FIG. 2 and FIG. 3 is a simple baseband representation. The symbol c to be transmitted is weighted with a transmit weighting vector v to form the transmitted signal vector. The received signal vector, x, is the product of the transmitted signal vector and the channel plus the noise. That is, X=Hs+n  (2) where the transmitted signals s is given by s=[s ₁ . . . s _(k)]^(T) =c[v ₁ . . . v_(k)]^(T),  (3) the channel is represented by H=[h ₁ . . . h _(k)],  (4) and the noise signal is expressed as n=[n ₁ . . . n _(k)]^(T).  (5)

The received signals are weighted and summed to produce an estimate, ĉ, of the transmitted symbol c.

In accordance with the principles of this invention and as illustrated in block 204 of FIG. 2, the transmit weighting factor, v, is set to $\begin{matrix} {v = {\frac{1}{a}\begin{bmatrix} h_{1} & \ldots & h_{K} \end{bmatrix}}^{H}} & (6) \end{matrix}$ where the superscript H designates the Hermitian operator, and a is a normalization factor given by $\begin{matrix} {a = \left( {\sum\limits_{k = 1}^{K}{h_{k}}^{2}} \right)^{1/2}} & (7) \end{matrix}$ is included in the denominator when it is desired to insure that the transmitter outputs the same amount of power regardless of the number of transmitting antennas. Thus, the transmitted signal vector (block 206 of FIG. 2) is $\begin{matrix} {s = {{cv} = {\frac{c}{a}\begin{bmatrix} h_{1} & \ldots & h_{K} \end{bmatrix}}^{H}}} & (8) \end{matrix}$ and the signal received at one antenna is x=Hs+n=ac+n  (9) from which the symbol can be estimated with the SNR of $\begin{matrix} {\gamma = {{a^{2}\frac{\sigma_{c}^{2}}{\sigma_{n}^{2}}} = {a^{2}\gamma_{0}}}} & (10) \end{matrix}$ where γ₀ denotes the average SNR for the case of a single transmitting antenna (i.e., without diversity). Thus, the gain in the instantaneous SNR is a² when using multiple transmitting antennas rather than a single transmitting antenna.

The expected value of γ is γ=E[a ²]γ₀ =KE└|h _(k)|²┘γ₀  (11) and, hence, the SNR with a K^(th)-order transmitting diversity is exactly the same as that with a K^(th)-order receiving diversity.

When more than one receiving antenna is employed, the weighting factor, v, is $\begin{matrix} {v = {\frac{1}{a}\quad\lbrack{gH}\rbrack}^{H}} & (12) \end{matrix}$ where g=[g₁ . . . g_(L)] (see block 204 of FIG. 2). The transmitted signal vector is then expressed as $\begin{matrix} {s = {\frac{c}{a}\quad\lbrack{gh}\rbrack}^{H}} & (13) \end{matrix}$ The normalization factor, a, is |gH|, which yields $\begin{matrix} {a = \left( {\sum\limits_{p = 1}^{L}{\sum\limits_{q = 1}^{L}{g_{p}g_{q}^{*}{\sum\limits_{k = 1}^{K}{h_{p\quad k}h_{qk}^{*}}}}}} \right)^{1/2}} & (14) \end{matrix}$ The received signal vector (block 304 of FIG. 3) is, therefore, given by $\begin{matrix} {x = {{\frac{c}{a}{H\quad\lbrack{gH}\rbrack}^{H}} + n}} & (15) \end{matrix}$

When the receiver's weighting factor, w, is set to be g (see blocks 306 and 308 of FIG. 3), the estimate of the received symbol is given by $\begin{matrix} {\overset{\_}{c} = {{gx} = {{{\frac{c}{a}\quad{{gH}\lbrack{gh}\rbrack}^{H}} + {gn}} = {{ac} + {gn}}}}} & (16) \end{matrix}$ with the overall SNR given by $\begin{matrix} {\gamma = {{\frac{a^{2}}{{gg}^{H}}\gamma_{0}} = \frac{a^{2}\gamma_{0}}{\sum\limits_{p = 1}^{L}{g_{p}}^{2}}}} & (17) \end{matrix}$

From equation (17), it can be observed that the overall SNR is a function of g. Thus, it is possible to maximize the SNR by choosing the appropriate values of g. Since the h_(qk) terms are assumed to be statistically identical, the condition that |g₁|=|g₂|=. . . =|g_(L)| has to be satisfied for the maximum value of SNR. Without changing the nature of the problem, one can set |g_(p)|=1 for simplicity. Therefore the overall SNR is $\begin{matrix} {\gamma = {\frac{a^{2}}{L}\gamma_{0}}} & (18) \end{matrix}$

To maximize γ is equivalent to maximizing a, which is maximized if $\begin{matrix} {{g_{p}g_{q}^{*}} = \frac{\sum\limits_{k = 1}^{K}{k_{p\quad k}k_{qk}^{*}}}{{\sum\limits_{k = 1}^{K}{k_{n\quad k}k_{nk}^{*}}}}} & (19) \end{matrix}$

Therefore, $\begin{matrix} {a = \left( {\sum\limits_{p = 1}^{L}{\sum\limits_{q = 1}^{L}{{\sum\limits_{k = 1}^{K}{h_{p\quad k}h_{qk}^{*}}}}}} \right)^{1/2}} & (20) \end{matrix}$ which results in the maximum value of γ. It is clear that the gain in SNR is $\frac{a^{2}}{L}$ when multiple transmitting and receiving antennas are used, as compared to using a single antenna on the transmitting side or the receiving side.

The vector g is determined (block 306 of FIG. 3) by solving the simultaneous equations represented by equation (19). For example, if L=3, equation (19) embodies the following three equations: $\begin{matrix} \begin{matrix} {{\left( {g_{1}g_{2}^{*}} \right) = \frac{\sum\limits_{k = 1}^{K}\quad{h_{1k}h_{2k}^{*}}}{{\sum\limits_{k = 1}^{K}\quad{h_{1k}h_{3k}^{*}}}}},} \\ {{\left( {g_{1}g_{3}^{*}} \right) = \frac{\sum\limits_{k = 1}^{K}\quad{h_{1k}h_{3k}^{*}}}{{\sum\limits_{k = 1}^{K}\quad{h_{1k}h_{3k}^{*}}}}},{\quad\quad}{and}} \\ {\left( {g_{2}g_{3}^{*}} \right) = \frac{\sum\limits_{k = 1}^{K}\quad{h_{2k}h_{3k}^{*}}}{{\sum\limits_{k = 1}^{K}\quad{h_{2k}h_{3k}^{*}}}}} \end{matrix} & (21) \end{matrix}$

All of the h_(pg) coefficients are known, so the three equations form a set of three equations and three unknowns, allowing a simple derivation of the g₁, g₂, and g₃ coefficients. The corresponding average SNR is given by $\begin{matrix} {\overset{\_}{\gamma} = {{E\left\lbrack a^{2} \right\rbrack}\frac{\gamma_{0}}{L}}} & (22) \end{matrix}$ where the value of E[a²] depends on the channel characteristics and, in general is bounded by LKE[|h_(k)|²]≦E[a²]≦βL²KE[|h_(k)|²]  (23) 

1. In a wireless communication system comprising transmitter apparatus for use with receiver apparatus wherein the transmitter apparatus comprises more than one antenna, a method of improving a signal to noise ratio of a transmission channel between the transmitter and receiver apparatus comprising: determining channel coefficients, h_(i), for each transmission channel between transmitter antennae and said receiver apparatus where i equals the number of transmitting apparatus antennae; determining a normalization factor from the determined channel coefficients; weighting each signal delivered to a transmitting antenna by a different weighting factor proportional to the inverse of the normalization factor; and maximizing signal to noise ratio such that the gain in signal-to-noise ratio by utilizing more than one transmit antenna is proportional to the square of the normalization factor.
 2. In a wireless communication system as recited in claim 1 further including receiver apparatus, said receiver apparatus comprising more than one antenna, the gain in signal-to-noise ratio being proportional to the square of the normalization factor divided by the number of receive antennae.
 3. A method as recited in claim 1 where the weighting factor comprises a vector of size equal to the number of transmit antennae.
 4. A method as recited in claim 1 where the weighting factor for each transmit antenna is equal to the conjugate of the corresponding channel coefficient, h_(i)*, divided by the normalization factor.
 5. A method as recited in claim 1 where the normalization factor a is given by the equation: $a = \left( {\sum\limits_{k = 1}^{K}\quad{h_{k}}^{2}} \right)^{\frac{1}{2}}$ where K is the number of transmit antennae and h₁ . . . h_(k) represent the channel coefficients.
 6. A method as recited in claim 3 wherein the weighting factor is a vector determined according to the equation ${v = {\frac{1}{a}\left\lbrack {h_{1}\quad\ldots\quad h_{K}} \right\rbrack}^{H}},$ where a is the normalization factor, K is the number of transmit anntennae and H is the Hermitian operator.
 7. A method as recited in claim 2 where the normalization factor a is given by the equation: $a = \left( {\sum\limits_{p = 1}^{L}\quad{\sum\limits_{q = 1}^{L}\quad{{\sum\limits_{k = 1}^{K}\quad{h_{pk}h_{qk}^{*}}}}}} \right)^{\frac{1}{2}}$ where K is the number of transmit antennae and L is the number of receive antennae.
 8. A method as recited in claim 1 wherein the channel coefficients are determined via a training session including transmitting pilot signals from each transmitting antenna to the receiving apparatus.
 9. A method as recited in claim 2 further comprising transmitting a symbol and estimating a value of the symbol at the receiving apparatus by weighting and summing the received signals by weighting factors for each receive antennae.
 10. Transmitter apparatus for use in a wireless communications system comprising a source of data symbols to be transmitted, a source of channel coefficient information for each channel to receiver apparatus, first and second multipliers coupled to the data symbol source and to the channel coefficient source, respective first and second antennae coupled to respective first and second multipliers for transmitting a data signal to said receiver apparatus, and means for computing a weighting factor for each transmission channel and for use at each of said first and second multipliers, each weighting vector being proportional to the inverse of a normalization factor and proportional to the channel coefficient data for a given transmission channel, the transmitted signal from respective antennae being the result of a multiplication by said multiplier of a data symbol to be transmitted and a respective, computed weighting factor for each transmission channel.
 11. Transmitter apparatus as recited in claim 10, where the weighting factor for each transmission channel is equal to the conjugate of the corresponding channel coefficient, h_(i)*, divided by the normalization factor.
 12. Transmitter apparatus as recited in claim 11, the multiplication of each symbol to be transmitted resulting in a gain in signal to noise ratio performance of the transmitter apparatus proportional to the square of the normalization factor.
 13. Transmitter apparatus as recited in claim 11, wherein the weighting factor is represented as a vector determined according to the equation ${v = {\frac{1}{a}\left\lbrack {h_{1}\quad\ldots\quad h_{K}} \right\rbrack}^{H}},$ where a is the normalization factor, K is the number of transmit antennae and H is the Hermitian operator and h₁ . . . h_(K) represent the channel coefficients.
 14. Transmitter apparatus as recited in claim 10, the normalization factor a is given by the equation: $a = \left( {\sum\limits_{k = 1}^{K}\quad{h_{k}}^{2}} \right)^{\frac{1}{2}}$ where K is the number of transmit antennae and h₁ . . . h_(K) represent the channel coefficients.
 15. Transmitter apparatus as recited in claim 10, the transmitter apparatus comprising a telecommunications system for use with receiver apparatus, said receiver apparatus comprising more than one antenna, the gain in signal-to-noise ratio being proportional to the square of the normalization factor divided by the number of receive antennae.
 16. A wireless communication method for transmitting data as symbols to a receiver, the method comprising: multiplying symbols to be transmitted via a multiplier for multiplying the symbol by a distinct weighting factor for each multiplier and an associated antenna, each multiplier being associated with an antenna of a plurality of K transmitting antennae, where K is greater than one; the weighting factor for a multiplier being proportional to a complex conjugate of the channel transfer coefficient for a channel between said associated transmit antenna and the receiver, and transmitting the weighted output symbols of the multiplier via said associated transmit antenna.
 17. A wireless communication method as recited in claim 16 wherein the weighting factor is given by the complex conjugate, h_(i)*, divided by a normalizing factor, a, which is $\left( {\sum\limits_{k = 1}^{K}\quad{h_{k}}^{2}} \right)^{\frac{1}{2}}.$ 